In the proposed work, global dynamics of a 3×6 system of rational difference equations has been studied in the interior of R+3. It is proved that system has at least one and at most seven boundary equilibria and a unique +ve equilibrium under certain parametric conditions. By utilizing method of Linearization, local dynamical properties about equilibria have been investigated. It is shown that every +ve solution of the system is bounded, and equilibrium P0 becomes a globally asymptotically stable if α1<α2,α4<α5, α7<α8. It is also shown that every +ve solution of the system converges to P0. Finally theoretical results are verified numerically.

We explore the equilibrium points, local and global dynamics, rate of convergence, instability and boundedness of positive solution of some rational systems of difference equations. As an application of difference equations in mathematical biology, we also explore the local dynamics about equilibrium points of the discrete‐time Levin's model. Finally, obtained results are verified numerically.

No abstract

In this paper, we explore the global dynamical characteristics, boundedness, and rate of convergence of certain higher-order discrete systems of difference equations. More precisely, it is proved that for all involved respective parameters, discrete systems have a trivial fixed point. We have studied local and global dynamical characteristics at trivial fixed point and proved that trivial fixed point of the discrete systems is globally stable under respective definite parametric conditions. We have also studied boundedness and rate of convergence for under consideration discrete systems. Finally, theoretical results are confirmed numerically. Our findings in this paper are considerably extended and improve existing results in the literature.

In this paper, global dynamical properties of rational higher-order system are explored in the interior of ℝ+3. It is explored that under certain parametric conditions, the discrete-time system has at most eight equilibria. By the method of linearization, local dynamics has been explored. It is explored that positive solution of the system is bounded, and moreover fixed point P000 is globally stable if α1/α2<1, α4/α5<1, α7/α8<1. It is also investigated that the positive solution of the system under consideration converges to P000. Lastly, theoretical results are confirmed by numerical simulation. The presented work is significantly extended and improves current results in the literature.